Absolute dynamical limit to cooling weakly coupled quantum systems

Here we address the question of just how cold one can cool a quantum system, given that the size of the control forces is limited. We solve this problem fully, within the dual regimes of (i) weak coupling, defined as that in which the thermalization dynamics of the system is preserved, and (ii) relatively strong control, being that in which appreciable cooling can be achieved. State-of-the art cooling schemes are presently implemented in this regime. Given that the maximum rate of coupling to the system is bounded, we identify a control protocol for cooling, and provide detailed structural arguments, supported by strong numerical evidence, that this protocol is globally optimal. From this we obtain simple expressions for the absolute limit to cooling. The methods developed can also be used to obtain optimal controls for a broad class of state-preparation problems.